8. Electric field lines arising from two small charged particles P and Q.
Consider the following two statements:
i.The charge on P is smaller than the charge on Q.
ii.The electrostatic force on P is smaller than that on Q.
Which of the above statements are true?
A) Only i. B) Only ii. C) Both i and ii.
the answer is A can you explain why its correct please and why B & C is wrong
The force on p and q is repulsive. pq/d^2. this is the same force on equal charge, opposing.
The answer A, which states that only statement i is true, is correct. Here's an explanation:
According to Coulomb's Law, the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
Where F is the electrostatic force, q1 and q2 are the charges of the particles, r is the distance between them, and k is the electrostatic constant.
Now, let's analyze each statement:
i. The charge on P is smaller than the charge on Q.
If the charge on P is smaller than the charge on Q (qP < qQ), using Coulomb's Law, we can conclude that the electrostatic force on P will be smaller than that on Q. This is because the force is directly proportional to the product of charges. Hence, statement i is true.
ii. The electrostatic force on P is smaller than that on Q.
This statement is not necessarily true. The electrostatic force depends on both the charges and the distance between the particles. It is possible for the charge on P to be larger than the charge on Q, but the distance between them could be such that the force on P is still smaller. Therefore, statement ii cannot be assumed to be true in general.
In conclusion, only statement i is true. The charge on P being smaller than the charge on Q guarantees that the electrostatic force on P will be smaller. Statements ii and iii cannot be inferred solely based on the relationship between the charges of P and Q.
To determine whether the given statements are true or false, we need to understand the relationship between the charges on P and Q and the resulting electrostatic forces.
The electric field lines arising from two small charged particles depend on the magnitude and polarity (positive or negative) of the charges on the particles. The direction of the electric field lines points away from positive charges and towards negative charges.
Statement i: The charge on P is smaller than the charge on Q.
If the charge on P is smaller than the charge on Q, this means that P has a lower magnitude of charge compared to Q. As a result, the electric field lines arising from P will be weaker than the electric field lines arising from Q.
Statement ii: The electrostatic force on P is smaller than that on Q.
The electrostatic force between two charged particles depends on the product of their charges and the distance between them. The force between two charges decreases as their separation distance increases; it increases as the product of their charges increases.
Given that the charge on P is smaller than the charge on Q, and assuming the separation distance is the same, the electrostatic force on P will be smaller than that on Q. This is because the force is directly proportional to the product of the charges.
Therefore, statement i is true because the electric field lines are weaker for P compared to Q, and statement ii is false because the electrostatic force on P is smaller than that on Q.
The correct answer is A) Only i.